A Statistical Perspective on Coreset Density Estimation

Paxton Turner, Jingbo Liu, Philippe Rigollet

Research output: Contribution to journalConference articlepeer-review


Coresets have emerged as a powerful tool to summarize data by selecting a small subset of the original observations while retaining most of its information. This approach has led to significant computational speedups but the performance of statistical procedures run on coresets is largely unexplored. In this work, we develop a statistical framework to study coresets and focus on the canonical task of nonparameteric density estimation. Our contributions are twofold. First, we establish the minimax rate of estimation achievable by coreset-based estimators. Second, we show that the practical coreset kernel density estimators are near-minimax optimal over a large class of Hölder-smooth densities.

Original languageEnglish (US)
Pages (from-to)2512-2520
Number of pages9
JournalProceedings of Machine Learning Research
StatePublished - 2021
Event24th International Conference on Artificial Intelligence and Statistics, AISTATS 2021 - Virtual, Online, United States
Duration: Apr 13 2021Apr 15 2021

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability


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